Boats and Streams -Solved Questions and Answers

Last Updated : 23 Sep, 2025

Boats and Streams deals with calculating the speed and travel time of a boat moving in a river or stream, where the water current affects its movement.

Downstream Motion: When the boat moves with the current.
Upstream Motion: When the boat moves against the current

Formula:

1. Downstream Speed = Boat Speed + Stream Speed
2. Upstream Speed = Boat Speed − Stream Speed
3. Boat Speed in Still Water:
Boat \ Speed = \frac {Downstream \ Speed \ + \ Upstream \ Speed}{2}
4. Stream Speed:
Stream \ Speed = \frac {Downstream \ Speed \ - \ Upstream \ Speed}{2}\frac{24}{b-2} and practice.

Question 1: A boat goes 24 km upstream and returns in 6.5 hours. During the return trip, the boat stops for 30 minutes due to engine trouble. If the stream’s speed is 2 km/h, find the boat’s speed in still water.

Solution:

Let b = boat speed in still water.
Effective time moving = 6.5−0.5=6 hours.
Upstream time = \frac{24}{b-2}.
Downstream time = \frac{24}{b+2}
Equation:\frac{24}{b-2}+\frac{24}{b+2}=6
simplify to quadratic equation b^2 - 8b - 4 = 0
b = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(-4)}}{2(1)}= \frac{8 \pm \sqrt{64 + 16}}{2}= \frac{8 \pm \sqrt{80}}{2}= {4 \pm 2\sqrt{5}}
Answer: 8.47 km/h

Question 2: Two boats A and B start simultaneously from opposite ends of a 60 km river. Boat A moves downstream, and Boat B moves upstream.
If: A’s speed in still water = 12 km/h,
B’s speed in still water = 8 km/h,
Stream speed = 4 km/h,
which boat reaches the other end first, and by how much time?

Solution:

A’s effective speed = 12+4=16 km/h.
Time = \frac{60}{16}=3.75 hours.
B’s effective speed = 8−4=4 km/h.
Time = \frac{60}{4}=15 hours.
Difference = 15−3.75=11.25 hours.
Answer: Boat A wins by 11.25 hours.

Question 3: A boat must reach a point 15 km upstream in 3 hours. The stream flows at 5 km/h. What is the minimum speed (in still water) the boat needs to achieve this?

Solution:

Required upstream speed =\frac{15}{3}=5 km/h.
Upstream speed = b−5.
Thus: b−5≥5⟹b≥10 km/h.
Answer: 10 km/h (any slower, and the boat can’t overcome the stream).

Question 4: A boat takes 1 hour longer to travel 20 km upstream than the same distance downstream. If the boat’s speed in still water is 10 km/h, find the stream’s speed.

Solution :

Let ss = stream speed.
Downstream time = \frac{20}{10+s}
Upstream time = = \frac{20}{10-s}
Given: = \frac{20}{10-s}-\frac{20}{10+s}=1
Solve for s (simplifies to s^2+40s−100=0).
Answer: 2.36 km/h (discard negative solution).

Question 5:Boat A (speed in still water = 15 km/h) starts 10 km behind Boat B (speed = 10 km/h) in the same direction downstream (stream speed = 2 km/h). How long will it take for Boat A to catch up?

Solution:

Effective speeds:
A: 15+2=17 km/h.
B: 10+2=12 km/h.
Relative speed = 17−12=5 km/h.
Time = \frac{10}{5}=2 hours.
Answer: 2 hours.

Question 6: A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water and the speed of the stream.

Solution:

We are given that speed downstream, D = 20 km/hr and speed upstream, U = 14 km/hr
Therefore, Speed of boat in still water = 0.5 × (D + U) km / hr = 0.5 × (14 + 20) = 17 km/hr
Also, speed of the stream = 0.5 × (D - U) km / hr = 0.5 × (20 - 14) = 3 km / hr
Another method:
Speed of the stream = 0.5 × (D - U) = 0.5 × 6 = 3 km / hr
Speed of the boat in still water = Speed of the stream + Speed Upstream = 3 + 14 = 17 km / hr

Question 7: A boatman can row a boat at the speed of 5 km/hr upstream and 15 km/hr downstream. Find the speed of the stream and the speed of the boat in still water.

Solution:

Let's denote:
B as Speed of the boat in still water (km/h)
S as Speed of the stream (km/h)
Speed of the boat upstream is the speed of the boat in still water minus the speed of the stream:
B − S = 5 km/hr...(i)
Speed of the boat downstream is the speed of the boat in still water plus the speed of the stream:
B + S = 15 km/hr...(ii)
Solving both equations
B = 10 km/h and S = 5 km/h
Hence, the speed of the boat in still water is 10 km/h
Speed of the stream is 5 km/h

Question 8: A man has to go from a port to an island and return. He can row a boat with a speed of 7 km/hr in still water. The speed of the stream is 2 km/hr. If he takes 56 minutes to complete the round trip, find the distance between the port and the island.

Solution :

Speed upstream = 7 - 2 = 5 km / hr
Speed downstream = 7 + 2 = 9 km / hr
Let the distance between the port and the island be D km. Also, we know that Time = Distance / Speed
⇒ (D/5) + (D/9) = 56/60
⇒ (14 D) / 45 = 56 / 60
⇒ D = 3 km
Therefore, the distance between the port and the island = 3 km

Question 9: In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

Solution:

Let the speed of the boat in still water be B km/hr
⇒ Speed upstream = (B - 2) km/hr
⇒ Speed downstream = (B + 2) km / hr
We know that Time = Distance / Speed
⇒ 6/(B-2) + 6/(B+2) = 4
⇒ 6 B + 12 + 6 B - 12 = 4 (B - 2) (B + 2)
⇒ 12 B = 4 (B - 2) (B + 2)
⇒ 3 B = B2 - 4
⇒ B2 - 3 B - 4 = 0
⇒ (B + 1) (B - 4) = 0
⇒ B = 4 km/hr (Speed cannot be negative)

Question 10: A racer can row a boat 30 km upstream and 44 km downstream in 10 hours. Also, he can row 40 km upstream and 55 km downstream in 13 hours. Find the speed of the boat in still water and the speed of the stream.

Solution:

Let the speed upstream be U km/hr and the speed downstream be D km/hr
We know that Distance / Speed = Time
⇒ (30 / U) + (44 / D) = 10 and (40 / U) + (55 / D) = 13
Solving the above pair of linear equations, we get
D = 11 km/hr
U = 5 km/hr
Therefore, Speed of boat in still water = 0.5 × (D + U) km / hr = 0.5 × (11 + 5) = 8 km / hr
Also, speed of the stream = 0.5 × (D - U) km / hr = 0.5 × (11 - 5) = 3 km / hr